Removing a few unwanted triangles and ngons/tsplines - is it necessary?
Here are some ideas to try, since I don't know what the parts of the mesh outside the viewport look like. 

For the first one: 
1. Add the green edge via the knife tool
2. Delete the red edge (or merge the verts so it's effectively gone)
3. Combine the triangles in the bluish triangle.



This will leave you with one triangle but the rest will be quads.  If you want to eliminate the triangle, you could try adding the yellow edge and then combining the resulting triangles and you'll have all quads. 

For the T-spline, I'd try to remove it if it were me.  If not, you're basically trusting Blender to deal with it because at some point it'll triangulate it internally to render, and it might not choose the edges ideally.  In this case there are many options, and any of the ones in this image would probably work ok.  Personally I'd probably go with the light blue one.



The green one is ok, but it will give you a triangle, if that matters.  The orange one would just give you a tiny triangle, but it might be small enough to not look bad.

Modeling is definitely an art and these might not be the perfect answers for your situation. I doubt it would affect your unwrapping even if you left it as-is, but your shading might be odd in the problem areas.  Hope this is helpful!